Thresholds in choice behaviour and the size of travel time savings

Transcription

1 Faculty of Transportation and Traffic Sciences, Institute for Transport and Economics Thresholds in choice behaviour and the size of travel time savings Session 45: Value of time II Andy Obermeyer (Co-authors: Martin Treiber, Christos Evangelinos) Toulouse, 6 th June 2014

2 Outline 1. Problem statement 2. Modelling approach 3. Application to synthetic data 4. Application to stated choice data 5. Conclusions Andy Obermeyer, TU Dresden 2

3 1 Problem statement Small travel time savings Travel time savings usually comprise a large part of economic benefits of transport infrastructure projects; often caused by small time savings for single persons. Are small travel time savings of lower, if any, unit value for individuals? There exist several arguments against using a discounted unit value for small travel time savings for project appraisal. It is not the aim of this presentation to assess these arguments Andy Obermeyer, TU Dresden 3

4 1 Problem statement Focus of our research Empirical issues in estimating time thresholds with discrete choice models. Consequence of ignoring them in model estimation: VTTS might be downward biased. This issue has to be addressed separately from the question whether time thresholds should be considered in benefit-cost analyses Andy Obermeyer, TU Dresden 4

5 2 Modelling approach What we want to model People can choose one of two alternatives (e.g. route choice). Standard binary choice model: People choose the alternative from which they obtain the highest utility. Utility (U) is decomposed into a deterministic (V) and a stochastic part (ε). Stochastic part is assumed to be i.i.d. Gumbel (logistically distributed differences). People may exhibit different sensitivities for small and large time differences. If this is the case, substitution between time and cost is different for small and large time changes. Model needs to reproduce different sensitivities for small and large time changes (below and above a threshold) Andy Obermeyer, TU Dresden 5

6 2 Modelling approach Form of transformation functions Andy Obermeyer, TU Dresden 6

7 2 Modelling approach Transformation functions f HTF ΔT, α HTF = 0 sign ΔT (abs ΔT α HTF ) abs(δt) < α HTF abs(δt) α HTF (1) f STF1 ΔT, α STF1 = ΔT α STF1 tanh ΔT α STF1 (2) f STF2 ΔT, α STF2 = ΔT 1 1 ΔT α STF (3) f Power ΔT, α Power = sign ΔT abs ΔT α Power (4) Andy Obermeyer, TU Dresden 7

8 3 Application to synthetic data Generating synthetic data Synthetic database with two alternatives and 5000 records. Utility difference calculated according to: ΔU ΔT, ΔC = ΔV ΔT, ΔC + Δε = β T f HTF ΔT, α HTF + β C ΔC + Δε Cost and time differences have been assumed to be independent and uniformly distributed in the range of [-10, 10 CHF] and [-25, 25 min], respectively. (5) Individual chooses alternative with the highest total utility (ΔU > 0 Individual choses alternative one) Andy Obermeyer, TU Dresden 8

9 3 Application to synthetic data Estimation Results I Andy Obermeyer, TU Dresden 9

10 3 Application to synthetic data Estimation results II Synthetic Linear HTF STF1 STF2 Power Cost * (0.12) * (0.83) * (0.92) * (0.92) * (0.92) Time * (0.00) * (0.47) * (0.35) * (0.26) (0.00) Alpha * (0.69) 6.34 * (0.45) 7.48 * (0.29) * [0.00] Null-LL Final-LL *, #, + Significant on 1%, 5% and 10% levels, respectively. (.) p-value for null hypotheses that parameter is equal to its target value. [.] p-value for null hypotheses that parameter is equal to one Andy Obermeyer, TU Dresden 10

11 3 Application to synthetic data Estimation results III HTF and the two STF fit really well and reproduce the target values. Despite the good fit of the power function the estimated time coefficient is significantly different from its target value. Linear specification has also been estimated to examine the error when ignoring the threshold. Time coefficient has not been reproduced correctly. Many observations are necessary to detect an existing threshold. For 5000 observations the log-likelihood difference between the linear and the threshold models is just about 9 units Andy Obermeyer, TU Dresden 11

12 4 Application to stated choice data Data Route choice experiments for commuting trips by train in Switzerland (from Swiss value of travel time study). Respondents had to choose between two routes which were characterised by the attributes travel time (T), travel cost (C), headway (H) and the number of changes (K) observations from roughly 180 respondents. Range of time differences varies from one minute to around 45 minutes with 20 per cent of the observations less than or equal to two minutes Andy Obermeyer, TU Dresden 12

13 4 Application to stated choice data Deterministic utility ΔV ΔT, ΔC, ΔH, ΔK, I, T λ I λ T + β H ΔH + β K ΔK = β T f r ΔT, α r + β C ΔC I I T T (6) λ I : Income elasticity (VTTS depends on income) λ T : Travel time elasticity (VTTS depends on travel time; journey length) Transformation functions described earlier applied (Power function omitted) Andy Obermeyer, TU Dresden 13

14 4 Application to stated choice data Estimation results I Andy Obermeyer, TU Dresden 14

15 4 Application to stated choice data Estimation results II Linear HTF STF1 STF2 Cost * * * * Time * * * * Alpha * # # Headway * * * * Changes * * * * Income Elasticity * * * * Time Elasticity * * * * Scale a [*] [*] [*] [*] Null-LL Final-LL LL-ratio test against Linear *, #, + Significant on 1%, 5% and 10% levels, respectively. [.] Significance level for null hypotheses that parameter is equal to one. a Controls for error scale differences. b Asymptotic value of travel time savings in CHF per hour Andy Obermeyer, TU Dresden 15

16 4 Application to stated choice data Estimation results III Across all three transformation functions, significant threshold parameters have been estimated threshold of two to three minutes. Likelihood-ratio tests show that the HTF and the STF are significantly better than the linear model. Horowitz (1983) - Test shows STF formulations perform not significantly worse than the HTF model Andy Obermeyer, TU Dresden 16

17 4 Application to stated choice data Value of travel time savings According to the threshold formulation VTTS is lower for small time changes and higher for large time changes in comparison to the linear model. VTTS = ΔC ΔT ΔV=0 60 [min/h] Consideration of thresholds leads to substantially higher asymptotic VTTS. Linear HTF STF1 STF2 VTTS (CHF/hr.) Andy Obermeyer, TU Dresden 17

18 5 Conclusions Conclusions based on synthetic data: Many observations are necessary to detect thresholds. HTF and STFs reproduce correct coefficients when thresholds are present (power function not). STF can easily be applied in any estimation tool for discrete choice analysis that can handle non-linear utility functions. Observations based on stated choice data: A time threshold between two and three minutes has been detected Andy Obermeyer, TU Dresden 18

19 5 Conclusions Implications for value of travel time savings: According to the threshold transformation functions the VTTS increases with the size of the time savings. If thresholds are not considered in a CBA the VTTS should be based on the asymptotic value of the threshold models (higher than the VTTS of a linear model). Do not ignore a threshold in the estimation procedure although it might not be included in project appraisal Andy Obermeyer, TU Dresden 19

20 We have seen in the previous slides time is money. Thank you very much that you have invested in this presentation Andy Obermeyer, TU Dresden 20